and Applied Analysis 3 ξ0,0,s,t (x) = ζ0,0,s,t = xs,t, ξ−1,0,s,t (x) = ζ−1,0,s,t (x) = xs−1,t, ξ0,−1,s,t (x) = ζ0,−1,s,t (x) = xs,t−1, ξ−1,−1,s,t (x) = ζ−1,−1,s,t (x) = xs−1,t−1. (7) Remark 1. If [Wσ]-limx = l, that is,

An associative information space contains all information relevant for a person organized using associations. Connecting such information spaces with each other allows the seamless integration of other’s information into our own. We believe this to be highly beneficial for group collaboration because it allows sharing of information in a very natural and efficient way without the need for a uni...

Symmetric spaces in the sense of E. Cartan supply major examples in Riemannian geometry. The study of their structure is connected closely to the theory of Lie groups. On these spaces, global analysis, particularly integration theory and theory of partial differential operators, arises in a canonical fashion by the requirement of geometric invariance. On R these two subjects are related to one ...

We extend the results of Mary Embry [9] on majorisation and range inclusion of bounded linear operators on Banach spaces to the case when one of the two operators is a convex process. An application in controllability is given.

We study weakly continuously Urysohn spaces, which were introduced in [Z]. We show that every weakly continuously Urysohn w∆-space has a base of countable order, that separable weakly continuously Urysohn spaces are submetrizable, hence continuously Urysohn, that monontonically normal weakly continuously Urysohn spaces are hereditarily paracompact, and that no linear extension of any uncountabl...

Following results of Bourgain and Gorelik we show that the spaces lp, 1 < p < ∞, as well as some related spaces have the following uniqueness property: If X is a Banach space uniformly homeomorphic to one of these spaces then it is linearly isomorphic to the same space. We also prove that if a C(K) space is uniformly homeomorphic to c0, then it is isomorphic to c0. We show also that there are B...

This paper establishes the equality of the observation spaces defined by means of piecewise constant controls with those defined in terms of differentiable controls. This research was supported in part by US Air Force Grant AFOSR-88-0235. keywords: Observation space, shuffle product, input-output system, generating series.